# Volumetric heat capacity

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Volumetric heat capacity (VHC) describes the ability of a given volume of a substance to store heat while undergoing a given temperature change, but without undergoing a phase change. It is different from specific heat capacity in that the VHC depends on the volume of the material, while the specific heat is based on the mass of the material. If given a specific heat value of a substance, one can convert it to the VHC by multiplying the specific heat by the density of the substance.

Dulong and Petit predicted in 1818 that ρcp would be constant for all solids (the Dulong-Petit law). In fact, the quantity varies from about 1.2 to 4.5 J/m3K. For fluids it is in the range 1.3 to 1.9, and for gases it is a constant 0.001 J/m3K.

The volumetric heat capacity is defined as having SI units of J/(·K). It can also be described in Imperial units of BTU/(ft³·).

## Engineer jargon: thermal inertia

thermal intertia is a term commonly used by engineers modelling heat transfers when referring to the volumetric heat capacity. For example, this material has a high thermal inertia. Or, thermal intertia plays an important role in this system, which means that dynamic effects are prevalent in a model, so that a steady-state calculation will yield unaccurate results.

It is more of an easy language shortcut than a real scientific analogy. In mechanics, inertia is what limits the acceleration of an object. Because of inertia you can't bring a car from 0 to 100 mph in 0.1 seconds. Similarly, in heat transfer, a higher value of the volumetric heat capacity means a longer time for the system to reach steady-state.

## Constant volume and constant pressure.

For gases it is useful to distinguish between volumetric heat capacity at constant volume and at constant pressure. This distinction has the same meaning as for specific heat capacity.